However I've never heard about the "check of consummation".
Well, as consummation was an important part of what made a marriage valid in the Middle Ages, it was important that witnesses saw the bridegroom and the bride going to bed together (like in this 15th century picture (don't worry, it is pretty tame and even has a priest blessing the newlyweds in their bed). The exact customs probably varied from region to region.
Of that I know. And if you want to refer to the bed of kings and queens, those were permanently attended anyway and so not much privacy there. Generally yes, there was this tradition of seeing the newly weds to bed, giving them the blessings, dressing them and so on, but my knowledge stops here. I don't believe there was an actual witnessing of the act by any of the parents or religious faces. In fact, that's what the bloody sheets were for, to provide proof of consummation. I also have never heard of a "next day virginity check". Again, the blood on the sheets would be sufficient evidence.
In early Middle Ages the royal (and, I suppose, high aristocracy - back then it could be hard to distinguish between the two, anyway) wedding consummation was, in fact, attended by several witnesses. It was a way of ensuring that a) the marriage was, in fact, consummated and b) it was consummated by the appropriate persons (see the stroy of Tristan and Iseult as an example of why it did not have to be the case) and any resulting offspring would have the required lineage. As far as I know (sorry, no citation, I'm referencing several books from memory and I'm at work anyway) it was not performed in view of all the guests, just a couple of highly respected officials, like the archbishop. I imagine the bride and groom were actually under some sort of covers. Later the bride and groom were just ceremoniuosly put in one bed, in their nightclothes, and there were no witnesses to any further proceedings. In fact, the further proceedings did not necessarily have to take place (see "The Six Wives of Henry VIII" by Antonia Fraser for example).
I have never heard of a tradition of stripping the newlyweds naked in front of all the guests. If there was such a tradition, it must have been very local.
There were various ways of checking the virginity of the bride. Still are, in fact. At Spanish Gypsy weddings (sorry, I'm not sure what is the official word for Gypsies now - Roms? Romany?) the eldest female in the grooms family performs the check using her finger and a white handkerchief. If there is blood, the feast may begin. Otherwise, there will be fighting.